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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 410, page id 1041163592:0444
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410
PHTLOSOPMISE NATDRALIS
D MuoBerior proportionalis sit motui Nodorum in Circulo, crit area
Srorenareprior proportionalis motui Nodorum in Ellipli. 8. F. D.
Corol. Igitur cum, in data Nodorum positione, summa omnium
arearum pD am, quo cempore Luna persit a Ouadratura 2d 10-
cum quemris m, sic arca mp  F d, qux ad FIlipleos tangencem
QF cerminatur; ec summa omnium arcarum illarum, in revolu-
cione inccora, sic area Fllipseos torius: motus medioeris Nodorum
in Ellipsi eric ad motum medioerem Nodorum in Circulo, vE PI.
lipsis ad Circulum; id cA, ut Z a 2d Y A, TOu 69 ad 70. PF
proxterea, cum mocus medioeris horarius Nodorum in Circulo
lic 2d 26. 35. 26. 36. ut AZ qu. 2d AT qu. St CapiaEUE augu-
IuS 16. 21. 3. 30. 2d angulum 16. 35. 10. 36. ut 69 2d 70,
erie motus medioeris horarius Nodorum in EllipA 2d 16. 21.
31. 30. Ut AZ g ad AFg; hoc est, ue quadratum sinus distancixe
Nodi a Solc ad quadratum Radii.
Cxeterum Luna, radio ad Terram ducco, aream reloeius descri-
bit in 5y2ygiis quam in Ouadraturis, ee eo nomine tempus in Sy-
Zygiis contrahitur, in Ouadraturis producitur; ec una cum tem-
Pore motus Nodorum ausetur ac diminuieur. Prat autem mo-
mentum arex in Ouadraturis Lunx ad ejus momentum in Syzygiis
UC 10975 ad 11073, e propterea momentum medioere in Octan-
tibus est ad excessum in Sy2rgiis, defectumquo in Quadraturis, ut
numerorum lemisumma +1023 ad corundem semidiftorentiam 50.
Onde cum tempus Lunx in singulis Orbis particulis aequalibus AE
reciproce ut ipsius relocitas, erit cempus medioere in Octantibus
ad excessum temporis in Ouadraturis, ac defectum in Syzygiis, ab
hac causa oriundum, uc 21023. 2d 50 quam proximo. P’ergendo
autem a Ouadraturis ad Syzrsias, invenio quod excessus momen-
torum areae in locis singulis, supra momentum minimum in Oua-
draturis, AE nE quadracum sinus distantixe Lunae a Onadraturis
quam proxime; ec propterea difterentia inter momentum in loco
quocunque ec momentum medioere in Octantibus, est ut diste
rentia incer quadratum sinus distantiae Lunaxe a Ouadraturis et
quadratum sinus graduum 45, scu semissem quadraci Radii; ee
incrementum cemporis in locis singulis incer Octantes et Guadra-
curas, ex decrementum ejus incer Octantes et Syzygias, eAt. in ca-
dem ratione. Mocus aurem Nodorum, quo tempore Luna per-
currie singulas Orbis particulas aequales, acceleratur vel retardatur
in duplicata racione temporis. FA enim mocus ilte, dum Luna
Der